# How to show that the number of jobs is distributed equally

Sorry if I'm asking an obvious question. I have proposed a load balancing algorithm for a system of several devices. Suppose at first the number of tasks on each device is $$device1 = 18$$, $$device2 = 8$$ and $$device3 = 2$$. Now after load balancing the number of tasks on each device has become $$device1 = 10$$, $$device2 = 8$$ and $$device3 = 10$$.

I want to publish the results and say that the number of tasks on devices is moderated after load balancing. I mean at first for example one device had $$18$$ tasks, while another had $$2$$ tasks, but after load balancing this amount is almost equal between all devices and it is almost $$10$$ which shows that these tasks are distributed almost equally.

But how can I state this in mathematical language? I was thinking about "the mean value of tasks" before and after load balancing, but then I saw that they are the same. So is there any mathematical way to show this difference in number of tasks before and after?

• Look up variance google.com/… – Ethan Bolker Jan 27 at 22:46
• @EthanBolker Thanks Ethan, I looked up variance and standard deviation and I found out useful information. So can I say that since after load balancing the value of standard deviation is lower than before load balancing, the load balancing is useful? I mean, in my case is it true that: the less the standard deviation is, the better the result is? – Pablo Jan 27 at 23:43
• That is a reasonable definition of the improvement your algorithm provides. – Ethan Bolker Jan 28 at 0:49